Question

A modulating signal is a square wave, as shown in the figure.

The carrier wave is given by $$$$$c(t) = 2\sin (8\pi t)$
A) Sketch the amplitude modulated waveform.
B) What is the modulation index?

Answer 1

To find the answer for this question, first we need to sketch the amplitude modulated waveform, the carrier wave is given from this amplitude carrier signal can be found, then the modulation index can be found easily.

Complete step by step answer:
Amplitude modulation is a kind of wave signal in which transmitted by modulation of amplitude by the signal it is often called as $AM$ and it is used in transmitting a piece of information by the radio carrier wave.

Amplitude modulation is used commonly in the form of electronic communication. In other words it is used to transmit and receive the message from one place to another in form of an electronic signal.

(A)Here the sketch of amplitude modulation waveform,

(B) The modulation index is otherwise called as modulation depth in which the modulated variable of the carrier signal varies around the unmodulated level. It is defined as the parameter in which determines the amount of modulation.
Modulation index is the ratio of amplitude of modulating signal to amplitude carrier signal.
$\mu = \dfrac{{{A_m}}}{{{A_c}}}$
the given modulation signal in which amplitude of the modulating signal ${A_m} = 1V$.
The carrier wave $e$ is given,
$e = 2\sin (8\pi t)$ $V$
Amplitude of the carrier wave ${A_c} = 2V$ is found from the equation.
Therefore the modulation index $\mu$ can be,
$\Rightarrow$ $\mu = \dfrac{{{A_m}}}{{{A_c}}}$
$\Rightarrow$ $\mu = \dfrac{1}{2}$
$\therefore$ $\mu = 0.5$

Note: The modulating signal can be used in broadcasting of radio. And also helps in larger signal to noise radio. It is used in telemeter, radar. Amplitude is also used in broadcast transmission. It is used in simple demodulation in which radio receivers capable of demodulating amplitude modulation are cheap and simple for manufacturing.